I've improved the reception on several small radios in a way that requires no modifications to the radio. The key is to build a large tuned loop antenna and then hold it nearby the portable radio. The antenna in the radio will couple to the large loop that you made, and pull in considerably more signal. It also functions to add some selectivity which can help reduce interference from other stations.
Going from memory, I recall building the loop using any insulated wire, but AWG18 enamelled copper is the ideal choice. Find a cardboard box or build a simple wooden frame that gives you a rectangle about 18 inches on each side and about 4 to 6 inches deep. The cardboard or wood has no electrical effect, so it can be anything that can hold the wire. Wind about 15 to 20 turns of wire around this form (wind so that each turn is an 18 inch by 18 inch square). The number of turns will have to found by experiment, but the method is easy, as you will see.
Next, you must find an old scrap AM radio and remove its variable tuning capacitor. These capacitors usually have two variables inside them, (and often the plastic housing is clear so you can see inside) one that is often about 360 pF and the other somewhat smaller. You need to find the two connection points to the larger capacitance. Usually you can do this by just looking at it and noting where the leads for the larger variable cap are brought out. Solder this variable capacitor to the two open ends of your coil and arrange a knob or handle on the capacitor so that you can rotate it.
That's about it. To use it, you place this large antenna near your radio, less than 12 inches is best. The loop has to be standing up on edge, not laying flat on a table. You first tune your radio to the station you want to hear. I usually start with a weak station in the middle of the band, say at about 1000KHz. Then I adjust the variable capacitor on my loop antenna. When the capacitor tunes to the radio's frequency, you will hear the volume of the station increase a lot (unless the station was already strong to begin with. That's why I start with a weak station). Once you have tuned the capacitor for loudest signal, you can physically move the large loop and the small radio to improve the signal strength. The large loop will receive strongest when a line going to the transmitting tower goes right through the axis of the loop.
If you find that there is no increase in signal as you rotate the capacitor, the reason may be that your soldering is not good enough, or it could be that we have the wrong amount of capacitance or the wrong number of turns of wire. First check that the capacitor is correctly soldered to the loop wire. You could try checking this by testing the resistance from one of the capacitor leads to the other. It should be close to zero. Also, make sure that none of the turns of wire are shorting against each other, this is why we use insulated wire.
Next, tune the radio to a weak station up near 1600KHz and then try tuning the loop again. If nothing happens, go down to another weak station near 600 KHz and try again. To get the loop to tune to a higher frequency, you have to reduce the capacitance or the number of turns of wire. To get it to tune to a lower frequency, you have to increase capacitance and/or increase the number of wire turns.